Projective Synchronization in Modulated Time-Delayed Chaotic Systems Using an Active Control Approach

Projective synchronization in modulated time-delayed systems is studied by applying an active control method. Based on the Lyapunov asymptotical stability theorem, the controller and sufficient condition for projective synchronization are calculated analytically. We give a general method with which we can achieve projective synchronization in modulated time-delayed chaotic systems. This method allows us to adjust the desired scaling factor arbitrarily. The effectiveness of our method is confirmed by using the famous delay-differential equations related to optical bistable or hybrid optical bistable devices. Numerical simulations fully support the analytical approach.